+980 Emily is twice as old as Charlotte. Four years ago, the product of their ages was 30. Use a quadratic equation to find Charlotte's present age.
First I said E (Emily) = 2C (Charlotte)
Then . . .
(E-4)*(C-4)=30
EC-4E-4C+16=30
EC-4E-4C=14
EC-4E-4C-14=0
Next I substituted in [E=2C]
(2C*C)-(2C*4)-4C-14=0
2C^2-8C-4C-14=0
2C^2-12C-14=0
Then I factorised . . .
2*(C^2-6C-7)=0
2*(C-7)*(C+1)=0
So Charlotte's present age must be 7.
To check it . . .
E=2*7=14
(E-4)*(C-4)=30
(14-4)*(7-4)=30
10*3=30
I thought this might interest at least one person.
+980 Nice 
I didn't think of doing it like that. The more direct route for sure.
+129918 Very nice, zacismyname !!! ....you're correct.....this is a good one !!!
We could also do it with one varable from the start :
Let Charlotte's age be x and Emily's age be 2x
So we have
(2x - 4)(x - 4) = 30
2x^2 - 12x + 16 = 30
2x^2 - 12x - 14 = 0
x^2 - 6x - 7 = 0
(x - 7) (x + 1) = 0 so x = 7 or x = -1 .....reject - 1 .....
So.....x = 7 = Charlotte's age and 2(7) = 14 = Emily's age
Just as you found !!!!
+980 Nice
I didn't think of doing it like that. The more direct route for sure.
